Results 31 to 40 of about 1,866,320 (298)
Parametric Evaluations of the Rogers-Ramanujan Continued Fraction
International Journal of Mathematics and Mathematical Sciences, 2011 In this paper with the help of the inverse function of the singular moduli we evaluate the Rogers-Ranmanujan continued fraction and its first derivative.
Nikos Bagis
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Generalized Hypergeometric Function 3F2 Ratios and Branched Continued Fraction Expansions
Axioms, 2021 The paper is related to the classical problem of the rational approximation of analytic functions of one or several variables, particulary the issues that arise in the construction and studying of continued fraction expansions and their multidimensional ...
Tamara Antonova +2 more
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Tasoev's continued fractions and Rogers–Ramanujan continued fractions
Journal of Number Theory, 2004 The author of this paper discusses Tasoev's continued fractions, which are of the form \[ [0;\underbrace{a,\dots,a}_m,\underbrace{a^2,\dots,a^2}_m, \dots]\equiv[0;\underbrace{\overline{a^k,\dots,a^k}}_m]_{k=1}^\infty,\;(m\geq1), \] and for a modified form he proves that \[ [0;\overline{ua^{2k-1}-1,1,va^{2k}-1}]_{k=1}^\infty=\frac{\sum_{s=0}^\infty u ...
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Continued Fractions and Linear Fractional Transformations
Integers, 2014 Rational approximations to a square root $\sqrt{k}$ can be produced by iterating the transformation $f(x) = (dx+k)/(x+d)$ starting from $\infty$ for any positive integer $d$. We show that these approximations coincide infinitely often with continued fraction convergents if and only if $4d^2/(k-d^2)$ is an integer, in which case the continued fraction ...
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Stability to perturbations of continued fraction approximants and applications
Researches in MathematicsThe paper investigates the problem of stability to perturbations of continued fraction approximants with complex elements. Unlike the problem of investigating the stability of continued fractions to perturbations, which focuses on the properties of ...
V. Hladun, M. Dmytryshyn
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On small vibrations of a damped Stieltjes string [PDF]
Opuscula Mathematica, 2015 Inverse problem of recovering masses, coefficients of damping and lengths of the intervals between the masses using two spectra of boundary value problems and the total length of the Stieltjes string (an elastic thread bearing point masses) is considered.
Olga Boyko, Vyacheslav Pivovarchik
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A certain method of construction of Thiele-Hermite continued fraction at a point
Pracì Mìžnarodnogo Geometričnogo Centru, 2023 The problem of interpolation of the function of a complex variable at a point of a compact set by the Thiele-Hermite continued fraction is investigated.
Mykhailo Pahirya, Yuliia Myslo
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Pediatric Blood &Cancer, EarlyView.ABSTRACT As part of the European Cooperative Study Group for Paediatric Rare Tumours initiative, we developed standard clinical practice guidelines for ovarian sex cord stromal tumors, based on comprehensive national and international cohort analyses, literature review, and a final expert consensus conference.
Dominik T. Schneider +15 more
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ON SMARANDACHE SIMPLE CONTINUED FRACTIONS [PDF]
, 1999 Starting with a Smarandache type sequence, showing that if A is a positive integer sequence, then the simple continued fraction is ...
Ashbacher, Charles, Le, Maohua
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Mathematics, 2022 Given real parameters a,b,c and integer shifts n1,n2,m, we consider the ratio R(z)=2F1(a+n1,b+n2;c+m;z)/2F1(a,b;c;z) of the Gauss hypergeometric functions.
Alexander Dyachenko, Dmitrii Karp
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